I am sorry no one is taking you seriously!! Come on guys where is your compassion for the hamster?
First off you should have mentioned it had been squished by a car or other heaving vehicle! Personally I would deal first with the overall shape of the hamster before trying to fix its leg. Easiest way to do this I would think would be too stuff it inside a toilet roll tube to give it back a more elongated hamster shape, I would cut 4 small holes in the tube and stick its legs through (does it only have two now? or are both sets of legs now squished together?).
I see little point helping it to walk before we fix its ears and give it back hearing, no point having it walk straight into a bionic cat ambush! Mechano might be a good start point as lego is more bulky! Also use small steppers from DSLR camera lenses that are used for auto focus etc, I have used a couple and they are pretty good, I am not too sure if they would work on a hamster wheel but worth a try.
Do you intend to fit a safety switch? I think with bionic legs a large red stop button should be included in case the legs get a short and legs go full chat on the wheel!! Best have a way for the hamster to stop this.
You also need to think of brakes, no good having a speedy hamster if it cant stop fast! When making the helmet make sure you allow enough room for when its cheeks are stuffed full, they tend to really bulge out when grabbing food. It might be better to fix a shredder in its mouth to stop it bulging its cheeks out.
My final thought is to use small watch cells, this is just because I can think of only one place to put the coin cells and still get to them, I think it kindest on the hamster to use the smallest cells you can get your hands on!!
Use gloves and grease when changing batteries please!